As the title of this course of lectures suggests, my aim was not a systematic treatment of infinite groups. Instead I have tried to present some of the methods and results that are new and look promising, and that have not yet found their way into the books of Kurosh, Specht, Zassenhaus, Marshall Hall, Jr. The contents of Chapters 8, 10, 11, 12 were mostly still unpublished at the time of the lectures; those of Chapters 8 and 12 have recently appeared. All through the lectures I have drawn attention to the numerous problems that still defy our efforts at solution. The Theory of Groups is still very much alive today. This course was delivered during the monsoon term, 1959, and extended over 36 lectures. I enjoyed every one of them. I am profoundly grateful to Professor K. Chandrasekharan for inviting me to spend this term at the Tata Institute of Fundamental Research. I also wish to record my gratitude to Mr. Pavman Murty, who took the notes and prepared them for circulation.

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